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Propagation in a fractional reaction-diffusion equation in a periodically hostile environment. (English) Zbl 07348197
Summary: We provide an asymptotic analysis of a fractional Fisher-KPP type equation in periodic non-connected media with Dirichlet conditions outside the domain. After showing the existence and uniqueness of a non-trivial bounded stationary state \(n_+\), we prove that it invades the unstable state zero exponentially fast in time.
MSC:
35R11 Fractional partial differential equations
35K20 Initial-boundary value problems for second-order parabolic equations
35K08 Heat kernel
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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